Modern commercial airliners are largely made of aluminum, a light and strong metal. But the fact that aluminum is cheap enough t

Question

4 months ago

15

Modern commercial airliners are largely made of aluminum, a light and strong metal. But the fact that aluminum is cheap enough t

hat airplanes can be made out of it is a bit of historical luck. Before the discovery of the Hall-Héroult process in , aluminum was as rare and expensive as gold. What would happen if airplanes had to be made of steel? The fuselage of the Airbus A380, which can carry passengers, is approximately a hollow aluminum cylinder without ends, long, wide, and thick (see sketch at right). The fuselage of an airplane Suppose this fuselage was made of steel (density ) instead of aluminum (density ), and let's say the average passenger has a mass of . We'll also assume the engines can't lift any greater mass than they already do. Calculate the number of passengers that the Airbus A380 could carry if its fuselage was made of steel.

Chemistry

1 answer:

lorasvet [2.7K] · Answer 1 · 2026-02-19T05:37:19+03:00

Respuesta:

Un avión fabricado con aluminio puede transportar una mayor cantidad de pasajeros comparado con uno de acero.

Explicación:

La masa total que el avión es capaz de levantar es:

$m_{tot}=m_{fuselage}+m_{passangers}$

Para el aluminio:

$m_{tot}=m_{fus-Al}+m_{pas-Al}$

$m_{fus-Al}=\delta _{Al}*V_{fuselage}$

y

$V_{fuselage}=\frac{\pi *L}{4}*[D^2-(D-e)^2]$

donde:

L es longitud
D es diámetro
e es grosor

$m_{tot}=\delta _{Al}*\frac{\pi *L}{4}*[D^2-(D-e)^2]+m_{pas-Al}$

Para el acero (mismo procedimiento):

$m_{tot}=\delta _{Steel}*\frac{\pi *L}{4}*[D^2-(D-e)^2]+m_{pas-Steel$

Sabiendo que la masa total que el avión puede levantar es constante y que el aluminio tiene una densidad menor que la del acero, podemos afirmar que el avión de aluminio puede levantar un mayor número de pasajeros.

También es posible estimar un peso promedio de los pasajeros para calcular cuántos podría soportar.